mlsanityData to 7 Oct 2026

Causal Bandits for Linear Structural Equation Models

arXiv 2208.12764 ↗First posted 26 Aug 2022stat.ML cs.LGcited by 19

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Abstract (arXiv)

This paper studies the problem of designing an optimal sequence of interventions in a causal graphical model to minimize cumulative regret with respect to the best intervention in hindsight. This is, naturally, posed as a causal bandit problem. The focus is on causal bandits for linear structural equation models (SEMs) and soft interventions. It is assumed that the graph's structure is known and has N nodes. Two linear mechanisms, one soft intervention and one observational, are assumed for each node, giving rise to 2N possible interventions. Majority of the existing causal bandit algorithms assume that at least the interventional distributions of the reward node's parents are fully specified. However, there are 2N such distributions (one corresponding to each intervention), acquiring which becomes prohibitive even in moderate-sized graphs. This paper dispenses with the assumption of knowing these distributions or their marginals. Two algorithms are proposed for the frequentist (UCB-based) and Bayesian (Thompson Sampling-based) settings. The key idea of these algorithms is to avoid directly estimating the 2N reward distributions and instead estimate the parameters that fully specify the SEMs (linear in N) and use them to compute the rewards. In both algorithms, under boundedness assumptions on noise and the parameter space, the cumulative regrets scale as tildecal O (d^L+frac12 √NT), where d is the graph's maximum degree, and L is the length of its longest causal path. Additionally, a minimax lower of Omega(d^fracL2-2√T) is presented, which suggests that the achievable and lower bounds conform in their scaling behavior with respect to the horizon T and graph parameters d and L.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 11 of its 32 references that are in the map. First posted on arXiv 26 Aug 2022.

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11 of 32 references.

References · 11

  1. 2016Causal Bandits: Learning Good Interventions via Causal Inferencecited by 100
  2. 2017Identifying Best Interventions through Online Importance Samplingcited by 39
  3. 2020Budgeted and Non-budgeted Causal Banditscited by 38
  4. 2021Causal Bandits with Unknown Graph Structurecited by 37
  5. 2018Causal Bandits with Propagating Inferencecited by 23
  6. 2022Adaptively Exploiting d-Separators with Causal Banditscited by 18
  7. 2018Contextual Multi-Armed Bandits for Causal Marketingcited by 17
  8. 2020Causal Bandits without prior knowledge using separating setscited by 17
  9. 2022Combinatorial Causal Banditscited by 16
  10. 2021A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounderscited by 15
  11. 2021Scalable Intervention Target Estimation in Linear Modelscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 5; 2025: 4; 2026: 3.

19 papers.

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  1. 2022Active Learning for Optimal Intervention Design in Causal Modelscited by 30
  2. 2022Model-based Causal Bayesian Optimizationcited by 26
  3. 2023Combinatorial Causal Bandits without Graph Skeletoncited by 7
  4. 2024Causal Bandits with General Causal Models and Interventionscited by 7
  5. 2023Learning Good Interventions in Causal Graphs via Coveringcited by 5
  6. 2024Linear Causal Bandits: Unknown Graph and Soft Interventionscited by 5
  7. 2026Reinforcement Learning in the Real World: A Survey of Statistical Challenges and Future Directionscited by 5
  8. 2023Robust Causal Bandits for Linear Modelscited by 4
  9. 2024Improved Bound for Robust Causal Bandits with Linear Modelscited by 2
  10. 2024Asymmetric Graph Error Control with Low Complexity in Causal Banditscited by 2
  11. 2025Graph Learning Is Suboptimal in Causal Banditscited by 2
  12. 2024Causal Contextual Bandits with Adaptive Contextcited by 1
7 more
  1. 2025Causal Bandit Over Unknown Graphs: Upper Confidence Bounds With Backdoor Adjustmentcited by 1
  2. 2025On Transportability for Structural Causal Banditscited by 1
  3. 2023Optimal Observation-Intervention Trade-Off in Optimisation Problems with Causal Structurecited by 0
  4. 2023Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Explorationcited by 0
  5. 2025Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanismscited by 0
  6. 2026Graph Structured Combinatorial Semi-Bandit with Nonlinear Reward Associations through Separable Signalscited by 0
  7. 2026On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Modelscited by 0